I usually lean towards Audio causing some issues, but if you have removed all the audio and it is still happening, I would suggest removing a single output from your GPU and test again for a few hours. If it still happens, remove the next output and test again. I have a feeling it might be the KVM sending some weird refresh data back to the GPU (power save maybe??) and that is causing some confusion? I would just start removing hardware piece by piece and see if you can find the culprit.
In terms of the larger video files my friend had issues with. It was something their content developed messed up in Adobe. HAd nothing to do with the encoding process. Just something I thought I would bring up as content can be a factor sometimes as well, But if it plays smooth from start to finish at least 1 time, then you can rule the content out of the mix.
